286 
directions of the coordinates, by which the point «, 7,2 has got 
! 
into a',y',2', then undergoes a shear ¢ in the ,z-plane, which 
at 
causes that point to be displaced to ev”, y", 2", Prof. Lorentz puts 
: dz! Oar" : 
AN (5 +5] and the increase of the density of energy 
& 2 
02" 0a" 4 s A 5 
aay + —-}, in which w is a coefficient of rigidity changed 
Oa! dz! ‘ 
by the preceding dilatations «, 2, y. Prof. Lorentz puts for this 
w=udtale + y) + 68. That @ and y only occur here in the com- 
bination «+ y is proved on the supposition that the tension \, 
02" dz” 
eee 
case, when we compare formulae (3) and (6), which give us the 
des Do. 
~ 
tensions for two deformations with equal — + =e. The proof 
Ow dz 
remains valid when we effect the shear according to (4); then, 
depends really only on which does not appear to be the 
however, the increase of energy is not given by 5 ue’, which we see 
by (5) and (6). In our problem, we must however shear according 
to (1). Then « and y do not occur any longer only in the combina- 
tion a+ y, and for the increase of energy we must use formula (2). 
Starting from this and following for the rest Prof. Lorrnrz’s 
reasoning, we come to the same result as Poynrina. 
Appendia by H. A. Lorentz. 
Mr. Tresninc is right. On account of an error in the reasoning 
of which | have made use in the note on p. 673 of my commu- 
nication, my formula (21) is not correct; it should run: 
u=—=u(l + 2z) 4+ a(x + 2) + by. 
Consequently in the expression derived from it for the change of 
the free energy per volume unity w (J + 2g + 2s) should be sub- 
stituted for u (1 + 2s), and in the second integral (22) + q for — q. 
Then u + a comes in the place of — ut + a, in the expression for 
(Q on p. 675, and equation (30) becomes: 
k GR? 
(A+ 2u)gq + 248 = — iw (u ga). 
If we replace in this, and also in (28) and (29): 
Oe seas pres a and h 
by Yi PO Oy oS AP as 2G; 
we get exactly the above formulae (8). 
I shall communicate on a later occasion what modifications my 
further caleulations now must undergo. | 
